Formation of α-iminoketones and α-diimines from aliphatic α,α′-dibromoketones

A novel reaction of aliphatic α,α′-dibromoketones with primary amines has been found to produce α-iminoketones and/or α-diimines, which can be selectively obtained under appropriate reaction conditions.     

Quantum-classical simulation of electron localization in negatively charged methanol clusters

A series of quantum molecular dynamics simulations have been performed to investigate the energetic, structural, dynamic, and spectroscopic properties of methanol cluster anions, [(CH(3)OH)(n)](-), (n = 50-500). Consistent with the inference from photo-electron imaging experiments, we find two main localization modes of the excess electron in equilibrated methanol clusters at ～200 K. The two different localization patterns have strikingly different physical properties, consistent with experimental observations, and are manifest in comparable cluster sizes to those observed. Smaller clusters (n ≤ 128) tend to localize the electron in very weakly bound, diffuse electronic states on the surface of the cluster, while in larger ones the electron is stabilized in solvent cavities, in compact interior-bound states. The interior states exhibit properties that largely resemble and smoothly extrapolate to those simulated for a solvated electron in bulk methanol. The surface electronic states of methanol cluster anions are significantly more weakly bound than the surface states of the anionic water clusters. The key source of the difference is the lack of stabilizing free hydroxyl groups on a relaxed methanol cluster surface. We also provide a mechanistic picture that illustrates the essential role of the interactions of the excess electron with the hydroxyl groups in the dynamic process of the transition of the electron from surface-bound states to interior-bound states.     

Topological Properties of the Set of Functions Generated by Neural Networks of Fixed Size

We analyze the topological properties of the set of functions that can be implemented by neural networks of a fixed size. Surprisingly, this set has many undesirable properties. It is highly non-convex, except possibly for a few exotic activation functions. Moreover, the set is not closed with respect to \(L^p\)-norms, \(0< p < \infty \), for all practically used activation functions, and also not closed with respect to the \(L^\infty \)-norm for all practically used activation functions except for the ReLU and the parametric ReLU. Finally, the function that maps a family of weights to the function computed by the associated network is not inverse stable for every practically used activation function. In other words, if \(f_1, f_2\) are two functions realized by neural networks and if \(f_1, f_2\) are close in the sense that \(\Vert f_1 - f_2\Vert _{L^\infty } \le \varepsilon \) for \(\varepsilon > 0\), it is, regardless of the size of \(\varepsilon \), usually not possible to find weights \(w_1, w_2\) close together such that each \(f_i\) is realized by a neural network with weights \(w_i\). Overall, our findings identify potential causes for issues in the training procedure of deep learning such as no guaranteed convergence, explosion of parameters, and slow convergence.

     

Analysis of localization sites for an excess electron in neutral methanol clusters using approximate pseudopotential quantum-mechanical calculations

We have used a recently developed electron-methanol molecule pseudopotential in approximate quantum mechanical calculations to evaluate and statistically analyze the physical properties of an excess electron in the field of equilibrated neutral methanol clusters ((CH(3)OH)(n), n=50-500). The methanol clusters were generated in classical molecular dynamics simulations at nominal 100 and 200 K temperatures. Topological analysis of the neutral clusters indicates that methyl groups cover the surface of the clusters almost exclusively, while the associated hydroxyl groups point inside. Since the initial neutral clusters are lacking polarity on the surface and compact inside, the excess electron can barely attach to these structures. Nevertheless, most of the investigated cluster configurations do support weakly stabilized cluster anion states. We find that similarly to water clusters, the pre-existing instantaneous dipole moment of the neutral clusters binds the electron. The localizing electrons occupy diffuse, weakly bound surface states that largely engulf the cluster although their centers are located outside the cluster molecular frame. The initial localization of the excess electron is reflected in its larger radius compared to water due to the lack of free OH hydrogens on the cluster surface. The stabilization of the excess electron increases, while the radius decreases monotonically as the clusters grow in size. Stable, interior bound states of the excess electron are not observed to form neither in finite size methanol clusters nor in the equilibrium bulk.     

Stable numerical solution of the Cauchy problem for the Laplace equation in irregular annular regions

This article is mainly concerned with the numerical study of the Cauchy problem for the Laplace equation in a bounded annular region. To solve this ill‐posed problem, we follow a variational approach based on its reformulation as a boundary control problem, for which the cost function incorporates a penalized term with the input data. The cost function is minimized by a conjugate gradient method in combination with a finite element discretization. In the case where the input data is noisy, some preliminary error estimates, show that the penalization parameter may be chosen like the inverse of the level of noise. Numerical solutions in simple and complex domains show that this methodology produces stable and accurate solutions.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1799–1822, 2017     

The adaptive buffered force QM/MM method in the CP2K and AMBER software packages

The implementation and validation of the adaptive buffered force (AdBF) quantum‐mechanics/molecular‐mechanics (QM/MM) method in two popular packages, CP2K and AMBER are presented. The implementations build on the existing QM/MM functionality in each code, extending it to allow for redefinition of the QM and MM regions during the simulation and reducing QM‐MM interface errors by discarding forces near the boundary according to the buffered force‐mixing approach. New adaptive thermostats, needed by force‐mixing methods, are also implemented. Different variants of the method are benchmarked by simulating the structure of bulk water, water autoprotolysis in the presence of zinc and dimethyl‐phosphate hydrolysis using various semiempirical Hamiltonians and density functional theory as the QM model. It is shown that with suitable parameters, based on force convergence tests, the AdBF QM/MM scheme can provide an accurate approximation of the structure in the dynamical QM region matching the corresponding fully QM simulations, as well as reproducing the correct energetics in all cases. Adaptive unbuffered force‐mixing and adaptive conventional QM/MM methods also provide reasonable results for some systems, but are more likely to suffer from instabilities and inaccuracies. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.